I think the best I can suggest - maybe cut it down a touch still would be from Hamlet...

HAMLET
I have of late--but
wherefore I know not--lost all my mirth, forgone all
custom of exercises; and indeed it goes so heavily
with my disposition that this goodly frame, the
earth, seems to me a sterile promontory, this most
excellent canopy, the air, look you, this brave
o'erhanging firmament, this majestical roof fretted
with golden fire, why, it appears no other thing to
me than a foul and pestilent congregation of vapours.
What a piece of work is a man! how noble in reason!
how infinite in faculty! in form and moving how
express and admirable! in action how like an angel!
in apprehension how like a god! the beauty of the
world! the paragon of animals! And yet, to me,
what is this quintessence of dust? man delights not
me

This is already cut down a touch, but I'm sure you can "accidentally" lose a few more parts to get it under a minute....

Well actually i'm already doing part of the first player's speech from Hamlet so I can't do another one from Hamlet. :/ That's a good speech though and it's one of the ones that made me fall in love with Hamlet.

Fair enough! Another suggestion could be to adapt a short scene between two or more characters to make into your own monologue - either by altering words to make it come across as "you" discussing with "yourself", or just taking the 2nd person's script away so speaking to an invisible and you just hear their response in your mind..?

I think I've just found a nice one for you! Morocco's lines from Merchant of Venice:-

O hell! what have we here?
A carrion Death, within whose empty eye
There is a written scroll! I'll read the writing.
"All that glitters is not gold;
Often have you heard that told:
Many a man his life hath sold
But my outside to behold:
Gilded tombs do worms enfold.
Had you been as wise as bold,
Young in limbs, in judgment old,
Your answer had not been inscroll'd:
Fare you well; your suit is cold."
Cold, indeed; and labour lost:
Then, farewell, heat, and welcome, frost!